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1. Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications

   https://doi.org/10.1103/PRXQuantum.5.040330  

   Moudgalya, Sanjay; Motrunich, Olexei I (November 2024, PRX Quantum)

   Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a “super-Hamiltonian.” We demonstrate this for conventional symmetries such as ${\mathbb{Z}}_2$, $U\left(1\right)$, and $SU\left(2\right)$, where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity-breaking phenomena of Hilbert-space fragmentation (HSF) and quantum many-body scars. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries, which in turn are related to slowly relaxing hydrodynamic modes in symmetric systems. This connection is made precise by relating the super-Hamiltonian to the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits and this physical interpretation also provides a novel interpretation for Mazur bounds for autocorrelation functions. We find examples of gapped (gapless) super-Hamiltonians indicating the absence (presence) of slow modes, which happens in the presence of discrete (continuous) symmetries. In the gapless cases, we recover hydrodynamic modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of $U\left(1\right)$symmetry, HSF, and a tower of quantum scars, respectively. In all, this demonstrates the power of the commutant-algebra framework in obtaining a comprehensive understanding of exact symmetries and associated approximate symmetries and hydrodynamic modes, and their dynamical consequences in systems with locality. Published by the American Physical Society2024 

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2. A QCD $R$ -axion

   https://doi.org/10.1103/PhysRevD.111.015048  

   Unwin, James; Yildirim, Tom (January 2025, Physical Review D)

   $R$-parity can be extended to a continuous global $\mathrm{U}(1{)}_R$symmetry. We investigate whether an anomalous $\mathrm{U}(1{)}_R$can be identified as the Peccei-Quinn symmetry suitable for solving the strong $CP$problem within supersymmetric extensions of the Standard Model. In this case, $\mathrm{U}(1{)}_R$is broken at some intermediate scale and the quantum chromodynamics axion is the $R$-axion. Moreover, the $R$-symmetry can potentially be gauged via the Green-Schwarz mechanism within completions to supergravity, in order to evade the axion quality problem. Obstacles to realizing this scenario are highlighted and phenomenologically viable approaches are identified. Published by the American Physical Society2025 

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3. Instantons in ${\varphi }^4$ theories: Transseries, virial theorems, and numerical aspects

   https://doi.org/10.1103/PhysRevD.110.036003  

   Giorgini, Ludovico T; Jentschura, Ulrich D; Malatesta, Enrico M; Rizzo, Tommaso; Zinn-Justin, Jean (August 2024, Physical Review D)

   We discuss numerical aspects of instantons in two- and three-dimensional ${\varphi }^4$theories with an internal $O\left(N\right)$symmetry group, the so-called $N$-vector model. By combining asymptotic transseries expansions for large arguments with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties is necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in ${\varphi }^4$theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations. Published by the American Physical Society2024 

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4. Dark Matter Axion Search with HAYSTAC Phase II

   https://doi.org/10.1103/PhysRevLett.134.151006  

   Bai, Xiran; Jewell, M J; Echevers, J; van_Bibber, K; Droster, A; Esmat, Maryam H; Ghosh, Sumita; Graham, Eleanor; Jackson, H; Laffan, Claire; et al (April 2025, Physical Review Letters)

   This Letter reports new results from the HAYSTAC experiment’s search for dark matter axions in our galactic halo. It represents the widest search to date that utilizes squeezing to realize subquantum limited noise. The new results cover $1.71\mathrm{\mu }\mathrm{eV}$of newly scanned parameter space in the mass ranges $17.28–18.44\mathrm{\mu }\mathrm{eV}$and $18.71–19.46\mathrm{\mu }\mathrm{eV}$. No statistically significant evidence of an axion signal was observed, excluding couplings $\left|g_{\gamma }\right|\ge 2.75\times \left|g_{\gamma }^{\mathrm{KSVZ}}\right|$and $\left|g_{\gamma }\right|\ge 2.96\times \left|g_{\gamma }^{\mathrm{KSVZ}}\right|$at the 90% confidence level over the respective region. By combining this data with previously published results using HAYSTAC’s squeezed state receiver, a total of $2.27\mathrm{\mu }\mathrm{eV}$of parameter space has now been scanned between $16.96–19.46\mathrm{\mu }\mathrm{eV}$ $\mu \mathrm{eV}$, excluding $\left|g_{\gamma }\right|\ge 2.86\times \left|g_{\gamma }^{\mathrm{KSVZ}}\right|$at the 90% confidence level. These results demonstrate the squeezed state receiver’s ability to probe axion models over a significant mass range while achieving a scan rate enhancement relative to a quantum-limited experiment. Published by the American Physical Society2025 

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5. Treelike structure of symmetry topological field theories and multisector QFTs

   https://doi.org/10.1103/PhysRevD.109.106013  

   Baume, Florent; Heckman, Jonathan J; Hübner, Max; Torres, Ethan; Turner, Andrew P; Yu, Xingyang (May 2024, Physical Review D)

   The global symmetries of a $D$-dimensional quantum field theory (QFT) can, in many cases, be captured in terms of a ( $D+1$)-dimensional symmetry topological field theory (SymTFT). In this work we construct a ( $D+1$)-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large $M$averaging where the topological sectors of different large $M$replicas become dressed by additional extended operators associated with the SymTree. Published by the American Physical Society2024 

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